Antisurge pretection method for centrifugal compressors

ABSTRACT

Method for individuating the pumping conditions of the centrifugal blowers according to thermo-dynamic conditions (pressure and temperature) and to the gas composition in inlet, comprising the steps of: acquisition of the suction pressure, the suction temperature, the delivery pressure, the delivery temperature, the flow rate, the revolution number and the chemical composition of the gas mixture; calculation of the reduced conditions of the processed gaseous mixture by means of mixing equations; solution of the state equation of the real gases for the calculation of the thermo not dynamic properties of the gas mixture in the current conditions; acquisition of the performance non-dimensional curves of the blower, which express the value of the working coefficient of the blower and of the plytropic yield of the blower; calculation of the blower performance curves on the basis of the non-dimensional curves and according to the blower inlet parameters; determination of the pumping points, individuated as maximum points of the blower performance curves which express the value of the pressure in outlet according to the sucked flow rate.

RELATED APPLICATIONS

This application is the U.S. National Stage under 35 USC 371 of PCT Application PCT/IB2012/053187.and claims foreign priority based of Italian patent application BA2011A000037.

BACKGROUND OF THE INVENTION

1. Field of the Invention

Object of the present invention is a new method for the protection of centrifugal blowers against the pumping phenomenon.

2. Brief Description of the Prior Art

The pumping phenomenon occurs when the blower works in a portion of its own characteristic curve, in the zone of low flow rates, where instable functioning conditions occur due to rapid variations of the flow rate processed by the machine, accompanied by a characteristic noise and high vibrations. Pumping is an abnormal functioning condition of the blower, which can become destructive and, in case of lack of suitable protection systems and if the machine remains in such a condition, which can lead to damage or breaking of the same blower or portions and components thereof. It is therefore useful to be able to diagnose promptly the approaching of a pumping condition, in order to take the suitable measures apt to avoid that such a condition occurs and continues. In the praxis, the systems dedicated to such a particular function are designed as anti-pumping systems. The anti-pumping systems are needed to protect the blower without providing excessively preventive control measures and running into penalizing working range reductions which lead to production losses, energy waste and consequent sharp reductions in the whole performance of the compression system, in addition to other possible consequences as, for example, the increase in gas recycle in torch, with consequent gas waste and increase in the relative atmospheric pollution inlet.

It is therefore useful to be able to diagnose promptly the approaching of such a pumping condition, in order to take the suitable measures apt to avoid that such a condition occurs or continues.

A measure known at the state of the art to avoid the pumping condition or forthcoming pumping condition is to open, partially or totally, a suitable control valve arranged on a line which recycles the delivery gas, cooled down, at the blower suction. In this way, it is reduced the whole resistance of the circuit, in which the compressor works, and the functioning point is moved to the right on the characteristic curve of the blower corresponding to the functioning number of revolutions. As a way of example, in FIG. 1 it is shown an example of characteristic curves of a blower (1001, 1002, 1003), relative to specific thermo-dynamic conditions of the gas which enters the same (pressure, temperature and chemical composition of the processed gas), designed on a plane having the volumetric flow rate and the delivery pressure as axes. Still in FIG. 1, the functioning zone is shown in the pumping condition, to the left of the pumping limit (1005) referred to the same suction conditions. A typical functioning point is indicated with (1006) in FIG. 1. In FIG. 2, it is shown a scheme of the system known at the state of the art in which it is provided a recirculation line (3) from the delivery (5) to the suction (4) of the blower (1) on which a control valve (2) is mounted.

All the traditional pumping protection systems apply a method based on the simplified determination of the locus of the pumping points determined in function of the following process parameters:

-   Ap₀ differential pressure on the measurement orifice in suction -   p₁ pressure in suction -   p₂ delivery pressure -   T₁ suction temperature -   T₂ delivery temperature

According to the current state of the art, the automatic protection systems determine, by means of simplified methods described in the following, the pumping condition by means of a relation, which, having defined the flow rate parameter

$\left( \frac{\Delta \; p_{o}}{p_{1}} \right)$

has the following general expression:

$\left( \frac{\Delta \; p_{o}}{p_{1}} \right)_{s} = {f\left( {g(\beta)} \right)}$

Where the subscript s indicates the pumping conditions

$\left( \frac{\Delta \; p_{o}}{p_{1}} \right)_{s}$

flow rate parameter in pumping condition), and g(β) is the compression parameter, function of the compression ratio β, defined as:

$\beta = \frac{p_{2}}{p_{1}}$

Now it is possible to indicate the functioning point of the blower with the coordinates

$\left( {\left( \frac{\Delta \; p_{o}}{p_{1}} \right),{g(\beta)}} \right).$

It is compared to the provided pumping point, having the coordinates

$\left( {\left( \frac{\Delta \; p_{o}}{p_{1}} \right)_{s},{g(\beta)}} \right).$

A PID regulator controls that the error

${\left( \frac{\Delta \; p_{o}}{p_{1}} \right)_{s} - \left( \frac{\Delta \; p_{o}}{p_{1}} \right)}$

is not lower than a safety margin, and provides the control of the anti-pumping valve by means of control techniques (PID) known by those skilled in the art.

In the following, there are enlisted documents describing the working methodology of the systems of the current state of art. In EP 0366216 it is described the implementation inside the control system of a simplified relation describing the place of the pumping points. Such a relation is described in form of linear connection between the parameter H_(red) and the parameter q²red defined as:

${Hred} = \frac{{Rc}^{\sigma} - 1}{\sigma}$ ${q^{2}{red}} = \frac{\Delta \; p_{o}}{p_{1}}$

Where:

R_(c) compression ratio σ exponent of the polytropic transformation occurring inside the blower. This method needs however that at least a pumping point is detected experimentally (page 5, line 39) in order to determine the grade of the linear relation between the parameters H_(red) and q²red. This grade depends also on the rotation speed. The thus determined straight line is normalized applying a transformation of variable such that the straight line is brought again to unitary grade (it should be noted that the straight line is not non-dimensionalised) and the pumping points are then indicated as all the points positioned on the thus individuated normalized straight line, indicated in FIG. 3, which expresses the relation:

H _(red) =k·q _(red) ²

EP 0366216 states that the just described method is able to determine the pumping points in all the working conditions, even if it admits that the pumping conditions are strongly influenced by the variations of the gas molecular weight, the specific heat and the blower efficacy. It is clear that what is described in the document EP 0366216 is the result of the application of exemplifying hypotheses, which can be accepted only roughly in a strict range of working design parameters of the blower. In particular, the gas is considered substantially ideal, and neither its chemical composition nor its thermo-dynamic properties are considered (coefficient of polytropic, isentropic, thermo-dynamic transformation, specific heat, molecular weight, viscosity etc.). The effects of compressibility, considered constant between the suction and delivery of the compressor are considered nonessential. In addition, the behavior of the real gas is ignored, it is in fact considered only the temperature polytropic exponent o and the most correct thermo-dynamic formulations providing for the real gas a double exponent of polytropic transformation n_(T) and n_(v) and a double exponent of isentropic transformation are ignored. Experimental researches (Kouremenos & Antenopoulos, “Isentropic Exponents of Real Gases and Application for Air at Temperatures From 150 K to 450 K”, Marie, Flow Measurement and Instrumentation 16 (2005), Schultz Journal of Engineering for Power, Vol. 84, 1962) highlighted as only by means of these coefficients it is possible to proceed to calculate correctly the thermo-dynamic properties of the processed gas mixture, and, by means of these ones, the blower performance.

In addition, the behavior of the blower i.e. the adjustment of the performance or functioning points of the blower (comprising the pumping points as well) is ignored. It is instead considered that for one and the same blower, the position of the pumping points can be determined by means of the “fluid dynamics affinity” relations:

Qαn; Hαn²

Where:

Q indicates the processed volumetric flow rate n indicates the number of revolutions of the blower H indicates the predominance provided by the blower .

As it is known, such relations are valid (suitably for incompressible flows) to anticipate the performance according to the variation of the machine revolution number only around a measured point. Also according to this limitation, the applicability of such relations remains limited to the inlet conditions (chemical composition, pressure and temperature) of the processed flow. Actually, by varying the latter, due to the complex connection between the descriptive equations of the blower performance and the dependence of these ones on the thermo-dynamic properties of the processed mixture, also the position of the pumping points will vary deviating from the expectations obtainable by an affinity law.

Notwithstanding such clear theoretical limitations, the traditional systems use such rough formulations mainly for the easiness of implementation and the instrumental easiness needed and for the relative calculation systems. The curves of the pumping points determined according to the modalities indicated in EP 0366216 appear independent from the chemical composition of the processed gaseous mixture and from the thermo-dynamic conditions of the same (pressure and temperature) only through the adopted exemplificative hypotheses. The method described is therefore limited and gives only one rough solution, as reported by the same text EP 0366216 (page 2, line 34), apt to avoid the reference to all those parameters which influence the problem considered difficult or impossible to be measured.

The same considerations can be made for U.S. Pat. No. 4,825,380, which is an example of a method for the diagnosis of the conditions of the forthcoming pumping which uses teachings substantially complying with what is yet described with minor variations. Also the document U.S. Pat. No. 7,094,019 relates to a method for the protection against pumping based on the measurement of the revolution number, pressure and inlet temperature, outlet pressure, which refers to the same rough formulations for determining the pumping points substantially according to what is stated in the document EP 0366219 and so with the same limitations. Other relevant documents can be considered, WO 2012/007553 or U.S. Pat. No. 6,364,602, but they have the same theoretical limits and no one of the them provides a method and technical solutions able to overcome the described limitation. It is to be noted that no one of these documents suggests the acquisition of the chemical composition of the processed gaseous mixture, or provides the calculation of the thermo-dynamic properties of the gaseous mixture according to the real gas theory, or makes use of specific information for the blower adjustment on the basis of which the performance of the same and in particular the pumping points can be anticipated.

Due to the used exemplificative hypotheses, in the systems of the current state of the art, the protection curves are considered independent from the inlet conditions of the blower (chemical composition of the compressed mixture and its thermo-dynamic conditions, pressure and temperature) and for this reason, sometimes, they are indicated as “universal surge lines”.

Actually, when deviating from the acceptability conditions of the adopted hypotheses, the protection curves are subjected to substantial variations. In the following, there are reported the results of a numerical analysis which shows as, by carrying out the calculations with the real gas thermo-dynamic theories and with the recent techniques of adjustment of the centrifugal blowers performances, the protection curves are subjected to substantial variations. In particular, it is possible to observe that, when equal to the compression parameter the flow rate parameter varies according to the variation of the inlet parameters at the blower. The following table shows the single and combined effect of the inlet parameters at the blower and the degree of error possible with the current protection systems in determining the pumping point. In the table, there are indicated some off design functioning conditions (Off design condition, “ODC”) with the relative variations with respect to the design condition (design condition, “DC”) in terms of inlet pressure variation (Δ.ρ′%), inlet temperature (ΔT) and molecular weight of the gas ΔM, as reported in Di Febo, Paganini, Esposito “Numerical Evaluation of centrifugal compressor surge locus modification with inlet parameters”.

ΔT p₂ Comparison Δp % [° C.] ΔM % p₁ error % DC - ODC 1 0 0 +20 1.5 5.5 2.7 6.8 DC - ODC 2 0 0 +48 1.5 16.2 2.7 18.6 DC - ODC 3 +6.5 0 0 1.5 1.5 2.7 2.1 DC - ODC 4 0 −15 0 1.5 3.4 2.7 4.1 DC - ODC 5 +6.5 −15 +48 1.5 27.6 2.7 31.2

It is observed that the error committed by accepting the exemplificative hypotheses of the current art is as more important as it deviates from the design conditions the most and in particular when it is processed in the high pressures and high compression ratios field. The importance of these errors detected through the numerical analysis is also confirmed by even catastrophic failures experiences which continue to occur in some cases due to the above described limitations of the protection capacity of the current systems.

Therefore, it is possible to state that the problem of the pumping protection is not definitely solved by the current technical solutions and that actually the pumping limitations depend on the gas mixture (therefore on its thermo-dynamic properties and still on its chemical composition) and on the relative thermo-dynamic conditions (pressure and temperature) at the blower inlet. Moreover, the pumping points depend on the blower type, so in order to identify correctly the same it is needed to provide a suitable adjustment of the machine, whose performance and functioning points (comprising the pumping points) in turn depend on the properties and chemical composition and thermodynamic conditions of the processed gas. The curves in FIG. 1 are in fact valid only for determined inlet conditions of the gas, and vary in a complex way according to the variation of pressure, temperature and gas composition in the same inlet. In the systems known at the state of the art, possible variations consequent to changes in the chemical composition of the gas sucked and to the conditions of pressure and temperature of the same are not detected by the algorithms and the protection remains still linked to the design conditions of reference, also when these are not those of the effective functioning, thus exposing the machine to possible damage or breaking.

SUMMARY OF THE INVENTION

Aim of the present invention is to provide a method for determining the pumping conditions which overcome the rough solutions linked to the methods yet described according to the state of the art, in order to provide an efficient protection of the blower while changing the working process conditions, comprising the variation of the chemical composition of the gas processed, the variation of the blower inlet pressure and temperature conditions and in function of the working point of the same (processed flow rate Q, revolution number n).

The protection system of the centrifugal blowers against the pumping phenomenon object of the present patent application provides a method and an apparatus able to protect the blower against the pumping phenomenon on the basis of the correct and in real time determination of the map of the blower performance and, in particular, of the pumping points.

According to another aim, the present invention provides a method for anticipating the blower performance in the effective functioning conditions in order to be able to compare them with the measured ones, providing an objective and quantitative reference for evaluating the blower performance, which can be used also for diagnostic finalities of the machine functioning state.

According to another aim, the present invention provides a device for the protection of centrifugal blowers against pumping which allows to protect the blower also in case of mechanic failure of the recirculation valve or of failure of the equipment and of the systems apt to detect the mechanic and/or thermo-dynamic parameters of the blower functioning.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

The present invention provides a method and an apparatus for the automatic protection against pumping and for the monitoring and the diagnostics of the centrifugal blower, comprising:

A. algorithms for determining the thermo-dynamic properties of the processed gaseous mixtures;

B. algorithms for determining the centrifugal blower performance (functioning points comprising pumping points) by means of;

aero-mechanic models of blowers based on non-dimensional performance parameters;

calculation models of the thermo-dynamic properties of the gaseous mixtures considered as real gas;

C. algorithms for the analysis of the blower functioning curves and for the pumping points individuation according to a physical criterion;

D. protection logics; thermo-dynamic anti-pumping protection and mechanic anti-pumping protection;

E. diagnostic logics; identification logics for problems about flow rate reading, blower mechanical problems, other problems of the equipment.

F. possibly the system can comprise means for determining the chemical composition of the compressed gas, intended as the mass or volume percentage of the chemical components constituting the gas.

G. In addition, the system object of the present invention, in order to provide an emergency intervention based ▪ on mechanic parameters independent form the process ones yet used as inlet, can comprise means for pumping detection based on the frequency analysis of the mechanic vibration of the blower shaft;

Referring to letter A in the above list and in FIGS. 5 and 6 appended, the method provided needs that the following data are known; suction pressure (Pi); suction temperature (T₁); delivery pressure (p₂); delivery temperature {T₂); sucked flow rate (Q); blower revolution number (n); molar composition of the gaseous mixture processed by the blower, expressed as mass or volume component percentage.

As a way of not limiting example, the components can belong to those enlisted in the following:

# Component 1 Argon 2 Carbon Dioxide 3 Carbon Monoxide 4 Ethane 5 Helium 6 Hydrogen 7 Hydrogen Sulfide 8 I-butane 9 I-pentane 10 Methane 11 N-buthane 12 N-decane 13 N-Heptane 14 N-exane 15 Nitrogen 16 N-nonane 17 N-octane 18 N-pentane 19 Oxygen 20 Propane 21 Water

Referring to the blower (1), to which the method is applied, the reference dimension (d₂) and the expressions of the following non-dimensional curves, shown in FIG. 8, are to be known:

η_(p)=ƒ(φ,Mu) “politrophic efficiency”;

η_(p)τ=ƒ(φ,Mu) “work coefficient”

Where

${\phi = {\frac{4}{\pi} \cdot \frac{Q}{d_{2}^{z} \cdot u_{z}}}};\mspace{14mu} {M_{u} = \frac{u_{2}}{\sqrt{k_{v\; 1} \cdot z_{1} \cdot R \cdot T_{1}}}};\mspace{14mu} {u_{2} = \frac{\pi \; {nd}_{z}}{60}}$

Such non-dimensional curves are available for different Mach numbers in suction at the blower. It is to be noted that such non-dimensional curves represent the aero-mechanic model of the blower, i.e. they keep the information about performance machine capacity while the different working conditions vary (chemical composition of the processed gas and respective thermo-dynamic conditions). Such curves are not to be confused with the normalized curves of the simplified and rough descriptions of the above cited patents.

If the non-dimensional curves are not available, for example because not included in the technical documents provided by the producer, the method according to the present invention provides the possibility to calculate the same by means of an inverted proceeding, starting form the following dimensional performance curves:

p ₂=ƒ(Q,n) or H _(p)=ƒ(Q,n); T ₂=ƒ(Q,n)

With H_(p), blower polytropic predominance, and starting from the reference conditions (molar composition, p₁, T₂) in which the dimensional curve are obtained. Such proceeding provides the inverted application of the equations reported in the following (page 18).

The calculation of the thermo-dynamic characteristics of the processed gaseous mixture (step A) provides a series of calculation steps, indicated in detail in FIG. 6. The processed mixture chemical composition being in inlet, and so the molar fractions of the components of the sucked mixture, and the thermo-dynamic conditions of the mixture being known both in inlet and outlet (p₁, T₁, p₂, T₂); the method provides the application of the mixing rules to determine the gaseous mixture parameters {v_(c), T_(c), critical gaseous mixture volume and temperature) according to the principle of the corresponding states.

In case of using gases containing hydrocarbons, there can preferably be implemented the mixing rules of Kay, modified by Lee-Kesler and then Plock, Knapp, Prausnitz et al. (1978). Other mixing rules can be used without reducing the method generalities. The usage of different mixing equations falls within the scope of the present invention. By means of the mixing rules, the algorithm determines the critical volume and temperature of the considered mixture and the reduced parameters of the considered mixture therefrom.

Some preferred formulations for the mixing rules known to those skilled in the thermo-dynamic field of the gaseous mixtures are reported in the following:

$\omega = {\sum\limits_{j}\; {x_{j}\omega_{j}}}$ $V_{c} = {\frac{1}{8}{\sum\limits_{j}\; {\sum\limits_{k}\; {x_{j}{x_{k}\left( {V_{cj}^{\frac{1}{3}} + V_{ck}^{\frac{1}{3}}} \right)}^{3}}}}}$ $T_{c} = {\frac{1}{8\; V_{c}^{\eta}}{\sum\limits_{j}\; {\sum\limits_{k}\; {x_{j}{x_{k}\left( \left( {V_{cj}^{\frac{1}{3}} + V_{ck}^{\frac{1}{3}}} \right)^{3} \right)}^{n}\sqrt{T_{cj}T_{ck}}\kappa_{j\; k}}}}}$

with

-   x, molar fraction -   ω, eccentric factor -   V_(c), component critical volume -   T_(c), component critical temperature -   k, binary interaction coefficients -   η, experimental coefficient -   i,j, gaseous mixture components indexes

If v_(c), T_(c) are known, it is possible to calculate the reduced parameters of the gaseous mixture p_(r), T_(r) and to proceed to the solution of the state equation for the specific gaseous mixture at the blower inlet. Preferably the method according to the present application can implement the state equation of Lee-Kesler where the final expression of the considered mixture compressibility coefficient z derives from a modification of the state equation of Benedict-Webb-Rubin (MBWR). Other state equations can be used without reducing the generalities of the proposed method. In the following, for reference rapidity, it is reported the state equation of Lee Kesler (B. I. Lee, M. G. Kesler. “A generalized thermo-dynamic correlation based on three-parameter corresponding states”, AiChE Journal 1975, 21 (3), 510-527).

$\mspace{20mu} {{Z = {{Z^{(0)}\left( {T_{r},P_{r}} \right)} + {\omega \; {Z^{(1)}\left( {T_{r},P_{r}} \right)}}}},{Z = {\left( \frac{P_{r}V_{r}}{T_{r}} \right) = {1 + \frac{f_{1}\left( T_{r} \right)}{V_{r}} + \frac{f_{2}\left( T_{r} \right)}{V_{r}^{2}} + \frac{f_{3}\left( T_{r} \right)}{V_{r}^{n}} + {{{f_{4}\left( T_{r} \right)}\left\lbrack {\left( {a + \frac{\gamma}{V_{r}^{2}}} \right)\frac{1}{V_{r}^{m}}} \right\rbrack}{\exp \left( {- \frac{\gamma}{V_{r}^{2}}} \right)}}}}},}$

ƒ_(1÷4), ∝, are functions and constants described in the reported references.

There are cited, without this being limiting, state equations suitable for the implementation of the system object of the present invention: LK (lee-Kesler), PR (Peng Robinson), RKS (Redlich-Kwong, Soave), B RS (Benedict-Webb-Rubin-Starling).

Therefore, by means of the real gas state equation, the thermo-dynamic properties of the gaseous mixture considered in function of the same molar composition are calculated. In the following, there are reported the differential formulations, well known to those skilled in the art, of the thermo-dynamic quantity resulting from the calculation step A, schematized in FIG. 6.

Specific heat at constant pressure (isobaric heat capacity)

$c_{p} = \left( \frac{\partial h}{\partial T} \right)_{s}$

Specific heat at constant volume (isochoric heat capacity)

$c_{v} = \left( \frac{\partial u}{\partial T} \right)_{v}$

Polytropic volume exponent (polytropic volume exponent)

$n_{v} = {{- \frac{v}{p}}\left( \frac{\partial p}{\partial v} \right)_{\eta_{p}}}$

Polytropic temperature exponent (polytropic temperature exponent)

$n_{T} = \frac{1}{1 - {\frac{p}{T}\left( \frac{\partial T}{\partial p} \right)_{\eta_{p}}}}$

Isentropic volume exponent (isoentropic volume exponent)

$k_{v} = {{- \frac{v}{p}}\left( \frac{\partial p}{\partial v} \right)_{s}}$

Isentropic temperature exponent (Isentropic temperature exponent)

$k_{T} = \frac{1}{1 - {\frac{v}{T}\left( \frac{\partial T}{\partial p} \right)_{s}}}$

Gas constant (Specific Gas constant)

R=R/M

Gas compressibility factor (Gas compressibility factor)

p·v=z−R·T

Optionally, the method can comprise the calculation of the compressed mixture viscosity, which is useful for the processed flow rate, according to the formulation reported in the following (IS05167/1)

$Q = {\frac{C}{\sqrt{1 - \beta^{4}}} \cdot ɛ \cdot \frac{\pi}{4} \cdot d^{2} \cdot \sqrt{{2 \cdot \Delta}\; {p_{o} \cdot p_{1}}}}$

Where the flow rate coefficient C has a different expression according to the device type used and it is function of the processed mixture viscosity.

It is observed that the anti-pumping protections proposed by the current art do not consider the fact that the real gas thermo-dynamic behaviour is described by the 2 polytropic transformation coefficients and by the 2 isentropic transformation coefficients reported, but they describe the thermo-dynamic transformation of the gaseous mixture by means of a single isentropic transformation coefficient “k” and a single polytropic transformation coefficient “n”. Actually such a condition occurs only in particular hypothesis, i.e. in the conditions of low pressure and high temperature where the real gas behaves as ideal gas. Substantially, the methods of the current art are based on the exemplificative hypothesis of ideal gas and ignore the calculation of the compressibility factor z.

FIG. 4 shows the values of coefficients k_(T) and k_(v) while the temperature varies, and for various pressure values for a specific gas. It is to be noted how the values differ with respect to each other while the pressure increases and the temperatures diminishes. Upon calculation of the thermo-dynamic properties of the processed mixture, the method proposed by the present application proceeds to the calculation of the blower performance. Such calculation is carried out on the basis of the availability of an aero-mechanic model of the blower constituted by the following non-dimensional curves, yet above described and reported in FIG. 8,

η_(p)=ƒ(φ,Mu), η_(p)τ=ƒ(φ,Mu).

Starting from such curves, by means of the steps indicated in FIG. 8, the performance curves of the blower are calculated:

p ₂=ƒ(Q,n), H _(p)=ƒ(Q,n), T ₂=ƒ(Q,n)

reported in FIG. 9.

The calculation of the dimensional curves of the blower is carried out by solving the following equation:

Hp = η_(p)τ ⋅ u₂² $\beta = \left\lbrack {1 + {\frac{H_{p}}{z_{1}{RT}_{1}} \cdot \frac{n_{V} - 1}{n_{v}}}} \right\rbrack$ $T_{2} = {T_{1} \cdot \beta^{\frac{n_{T} - 1}{n_{T}}}}$ p₂ = p₁ ⋅ β

The solution of such calculation proceedings,

-   repeated for different values of flow rate -   coefficients ψ, allows to trace the performance curves yet reported:

p ₂=ƒ(Q,n); H _(p)=ƒ(Q,n); T ₁=ƒ(Q,n)

These ones are calculated for different blower revolution numbers, in particular for the current revolution number.

Therefore, the obtained curves represent all the functioning points of the blower, comprising the pumping points. In order to determine these points, letter C in FIG. 5, there are analyzed the dimensional curves of the blower, on which as pumping points there are individuated the points satisfying the following equation:

$\frac{\partial p_{2}}{\partial Q} = 0$

Such equation implements a physical criterion of pumping occurrence which does not need the experimental determination of any pumping points. By means of the calculation steps of letter A and C in FIG. 5, it is reached a determination of the pumping points which is not influenced by the errors introduced in the approximations applied to the methods of the current technique. Once the pumping points are determined according to the method proposed, there can be conveniently used techniques for controlling the recirculation vale (2) in FIG. 11, which are known at the state of the art to protect the blower against the pumping phenomenon. The proposed method and apparatus object of the present application, knowing the chemical composition of the processed gas mixture, apply all the thermo-dynamic theories available for the real gases and for modeling the blowers to determine previously, and in real time, the pumping points of the blower in the current working conditions and with the process gas actually sucked by the blower.

Moreover, the method proposed can make use of the capacity to anticipate correctly the blower performance to allow the comparison of the expected performance with the current ones expressed by the blower and so to carry out a diagnostics of the same blower functionality. From the comparison, it is possible in fact to evaluate if the machine is working according to the design or not and to decide, by means of suitable logics which will be described in the following, if there are any problems of mechanic nature causing the possible differences detected or if there can be any instrumental problems. This kind of diagnostics is possible only where it is available the capacity of correct anticipation of the blower current performance. Such capacity is not available in the traditional systems.

The algorithms of the system which implement diagnostic functionalities receive in real time both the data concerning the current blower performance and the performance expected upgraded according to the current functioning conditions (mixture chemical composition and relative pressure and temperature).

By the term “expected” it is intended a working parameter obtained by means of the blower performance curves upgraded to the current functioning conditions according to what above described.

For example, with a flow rate Q known, on the basis of current conditions (composition, pressure and temperature), it will be possible to obtain the expected pressure p₂ and the temperature T₂ from the performance curves upgraded to the same.

Vice versa, with the pressure p₂ or the temperature T₂ being known, from the expected curves it is possible to obtain the expected flow rate Q.

Another feature of the system proposed consists in the possibility of the control and possible exclusion of the flow rate measure. As it is known, in many industrial installations, the flow rate measure is subjected to peculiar problems due to which it can result affected by error. In the traditional systems, an error about the flow rate reading produces a lack of protection concerning pumping and for this reason, in these cases, it is usually decided the system stop with consequent impacts on the production and therefore on the system economy.

The system object of the present application allows to obviate such problem, as it offers the possibility to detect problems of instrumental nature upon flow rate reading and to arrange, in such cases, the substitution of the measured flow rate (considered wrong) with the expected flow rate as previously defined in all the blower protection logics.

The criterion for the exclusion of the flow rate is described in detail in FIG. 10. When the system detects that the expected delivery pressure (p2_(EXP)) and the measured delivery pressure (p2_(MEAB)) differ with respect to each other, and/or that the expected delivery temperature (T2_(EXP)) and the measured delivery temperature (T2_(MEA)B) differ with respect to each other, FIG. 10, it proceeds to compare the expected flow rate according to the measured delivery pressure (Q2_(EXP)@P2_(MEAB)) and the expected flow rate according to the measured delivery temperature (Q2_(exp@T)2_(MEAB)). In case that such values are equal, the system identifies a problem of wrong reading of the flow rate and provides a consequent diagnostic signal. In this case, as reference value the system assumes the value of the expected flow rate according to the measured delivery pressure (Q2_(EXP)@P2_(MEAB)) for the calculations concerning the anti-pumping protection.

In the opposed case, i.e. if Q2_(EXP)@P2_(MEAB) differs from Q2_(EXP)@T2_(MEAB) the system proceeds to verify if Q_(EXP)@P2_(MEAB) is greater than Q2_(EXP)@T2_(MEAB). In such a case, the system attributes the difference to a mechanic degradation of the blower, i.e. to a reduction of the polytropic yield on the whole working field, and provides a corresponding diagnostic signal. If instead, Q_(EXP@)P2_(MEAB) is smaller than Q2_(EXP)@T2_(MEAB) the system attributes the difference detected to a problem of instrumental nature and provides a corresponding diagnostic signal.

Thanks to such a capacity of the system, the blower can be maintained running also in presence of an error of flow rate reading, with the consequent clear advantages of working and economic kind.

The apparatus needed for the implementation of the method according to the present invention comprises:

-   1. means for measuring the process parameters: suction pressure     (p₁); suction temperature (T₁); delivery pressure (p₂); delivery     temperature (T₂); sucked flow rate {Q); blower revolution number     (n); optionally, the apparatus can comprise means for determining     the chemical composition of the gaseous mixture and means for the     treatment of the signals acquired by said means, yet optionally,     there can be provided means for the detection and the analysis of     the mechanic vibration signal of the blower shaft. -   2. Processors provided with high calculating capacity, for carrying     out the algorithms for the solution of various calculation steps     described (solution of the mixing rules, solution of the state     equations and calculation of the thermodynamic properties of the     gaseous mixtures, modeling of the centrifugal blower and     determination of the pumping points, diagnostic logics). -   3. Calculators for the implementation of the sequences and PID     control logics of the control valve.

Conveniently, the apparatus can comprise a communication software and interface between the various processing systems and user interface devices.

Preferably, the thermo-dynamic calculation steps described can be carried out on a dedicated calculator, which is added to the systems (generally of PLC type) which has to carry out the protection logics and the anti-pumping valve control. Therefore the proposed system can be preferably implemented with a calculation server which dialogues with the control system communicating thereto the information about the calculated pumping points referring to the current conditions and about the expected performance for the blower referring to the current conditions.

The calculation algorithms are apt to determine the information needed to the protection logics according to the described calculation steps. Such information is exchanged between the two processing systems by means of suitable communication protocols.

As it can be noted in FIG. 11, the device for determining the forthcoming pumping conditions according to the present invention comprises the same means for measuring the flow rate (10), pressure (11) and temperature (12) in inlet, the pressure (14) and temperature (15) in outlet and the revolution number (13) provided by the current technique. In addition, the device according to the present invention can be provided with means for determining the gas chemical composition in inlet (9), as for example a gas chromatograph in line. Alternatively, according to the application in which the blower to be protected is used, and in particular in the cases in which the molar composition is slowly variable, the upgrading of the gas composition in inlet can be provided in inlet on the basis of periodical off line analyses (8).

Optionally, the device can comprise means for the acquisition of a vibration signal of mechanic nature (17) and means (18) for the frequency analysis of said signal and the control in override mode of the anti-pumping valve (2).

In addition the system is provided with calculation means (16) for carrying out the thermo-dynamic algorithms, interconnected to the calculation and control means (6) of the anti-pumping valve (2). By means of the described algorithms, implemented through the calculation means (16) it is possible to calculate in real time the pumping points of the blower to be protected, upgraded with respect to the current working conditions, i.e. with respect to the gas with current chemical composition and relative suction pressure and temperature (pi, Ti). The information about the current pumping point is transmitted by said calculation means (16) to said calculation and control means (6) of the anti-pumping means (2), by means of which it is carried out a continuous control of the same valve.

In fact, when the previously described referring to the diagram of FIG. 5 calculation step of the pumping points in the current conditions is ended, it is possible to compare the measured flow rate with the expected limit pumping flow rate, to determine if the functioning conditions are sufficiently far from the pumping, or if it is needed to intervene on the anti-pumping valve, and therefore to send a control signal to the same valve.

Conveniently, the described protection logic can be provided also with another independent protection feature, which controls the anti-pumping valve on the basis of data deriving from the frequency analysis (FFT) of a signal of mechanic nature detected on the blower.

Said signal of mechanic nature can be for example a radial vibration signal obtained from the proximity feelers installed at one of the bearings which bear the blower shaft, as provided for example from the standard of the petrol field. Clearly, it can be used any type of sensor (accelerometer, parasitic current sensor etc.) able to detect the vibrations at the significant points of the blower without departing from the scope of the present invention. The thus acquired vibration signal is a signal indicating a phenomenon of mechanic type, for the processing of which there are needed measures or considerations of thermo-dynamic kind or of blower modeling, and therefore it is efficient to guarantee the protection in case of error of the described thermo-dynamic protection. The vibration signal is acquired by the system and analyzed in the frequency domain (FFT) according to techniques known at the state of the art. From the frequency spectrum, only the sub-synchronous components connected to the pumping are filtrated. The frequencies at which these components can be depend on the blower model used and on the relative installation conditions, and can be detected with suitable field tests. Generally, low frequency vibrations can be considered connected to the pumping. As a way of purely illustrative and not limiting example, it can be said that the frequency value of such vibrations can be comprised between 5 and 20 Hz, preferably between 8 and 10 Hz. The intensity of the sub-synchronous vibration components is sent to a suitable regulator which carries out the control of the anti-pumping valve in “override” mode (known to those skilled in field of control techniques), with respect to the other controllers acting on the same. The same signal containing the intensity of the sub-synchronous vibrations is compared with a predetermined safety level and, if the intensity of the sub-synchronous frequencies persists beyond said safety level for a defines interval, it is decided the blower stop. Moreover, the detection of abnormal pumping sub-synchronous vibration components leads to the automatic adjustment of the functioning point in which the pumping and the upgrading of the anti-pumping protection occurred. 

1. Method for individuating the pumping conditions of centrifugal blowers according to the thermodynamic conditions (pressure and temperature) and to the gas composition in inlet, comprising the steps of: a) acquisition of the suction pressure (pi), the suction temperature (TI), acquisition of the delivery pressure (p2), the delivery temperature (T2), the flow rate (Q), the revolution number (n) and of information about the chemical composition of the gas mixture in inlet at the blower (1); b) calculation of the reduced conditions of the processed gaseous mixture by means of mixing equations; c) solution of the state equation of the real gases for the calculation of the thermo-dynamic properties of the gas mixture in the current conditions acquired at the previous point (a). d) acquisition of the performance non-dimensional curves of the blower, which express the value of the blower working coefficient and of the polytropic yield of the blower, according to the Mach number in inlet and to the flow rate parameter; e) calculation of the blower performance curves which express the value of pressure and temperature in outlet (2, T2) and of the polytropic predominance {Hp) according to the flow rate and. the revolution number, on the basis of said performance non-dimensional curves acquired at point d), and according to the blower inlet parameters acquired at point a) f) determination of the pumping points, individuated as maximum points of the blower performance curves which express the value of the pressure in outlet according to the sucked flow rate, and according to the variation of the revolution number.
 2. Method for individuating the pumping conditions of centrifugal blowers according to claim 1, wherein said calculation of the reduced conditions of the gas mixture at the blower inlet is carried out by applying the “mixing rules” of Kay, modified by Lee-Kesler and Plock, Knapp, Prausnitz et al. (1978).
 3. Method for individuating the pumping conditions of centrifugal blowers according to claim 1, wherein said thermo-dynamic properties of the mixture calculated at point c) comprise the following ones: Polytropic volume exponent $n_{v} = {{- \frac{v}{p}}\left( \frac{\partial p}{\partial v} \right)_{\eta_{p}}}$ polytropic temperature exponent $n_{T} = \frac{1}{1 - {\frac{p}{T}\left( \frac{\partial T}{\partial p} \right)_{\eta_{p}}}}$ isentropic volume exponent $k_{v} = {{- \frac{v}{p}}\left( \frac{\partial p}{\partial v} \right)_{s}}$ Gas molar constant R=R/M Gas compressibility factor (z) p·v=z·R·T.
 4. Method for individuating the pumping conditions of centrifugal blowers according to claim 3, wherein said thermo-dynamic properties are calculated using a state equation of real gases, preferably between the following ones: LK (lee-Kesler), PR (Peng Robinson), RKS (Redlich-Kwong, Soave), BWRS (Benedict-Webb-Rubin-Starling), for example the state equation of Lee Kesler (B. I. Lee, M. G. Kesler. “A generalized thermo-dynamic correlation based on three-parameter corresponding states”, AiChE Journal 1975, 21 (3), 510-527). $\mspace{20mu} {{Z = {{Z^{(0)}\left( {T_{r},P_{r}} \right)} + {\omega \; {Z^{(1)}\left( {T_{r},P_{r}} \right)}}}},{Z = {\left( \frac{P_{r}V_{r}}{T_{r}} \right) = {1 + \frac{f_{1}\left( T_{r} \right)}{V_{r}} + \frac{f_{2}\left( T_{r} \right)}{V_{r}^{2}} + \frac{f_{3}\left( T_{r} \right)}{V_{r}^{n}} + {{{f_{4}\left( T_{r} \right)}\left\lbrack {\left( {a + \frac{\gamma}{V_{r}^{2}}} \right)\frac{1}{V_{r}^{m}}} \right\rbrack}{\exp \left( {- \frac{\gamma}{V_{r}^{2}}} \right)}}}}},}$ ƒ_(1÷4), ∝, are functions and constants described in the reported references.
 5. Method for individuating the pumping conditions of centrifugal blowers according to claim 1, wherein said calculation of the blower performance curves which express the value of pressure and temperature in outlet, and the polytropic predominance, in function of the flow rate and the revolution number is carried out, with the curves known, η_(p)=f(φ,Mu), η_(p)τf(φ,Mu) known, with $M_{u} = {{\frac{u_{2}}{\sqrt{k_{v\; 1} \cdot z_{1} \cdot R \cdot T_{1}}}\phi} = {{{\frac{4}{\pi} \cdot \frac{Q}{d_{2}^{2} \cdot u_{2}}}u_{2}} = \frac{\pi \; {nd}_{2}}{60}}}$ according to the following calculation steps: $\begin{matrix} {{Hp} = {\eta_{p}{\tau \cdot u_{2}^{2}}}} & \left. a \right) \\ {\beta = \left\lbrack {1 + {\frac{H_{p}}{z_{1}{RT}_{1}} \cdot \frac{n_{V} - 1}{n_{V}}}} \right\rbrack} & \left. b \right) \\ {p_{2} = {p_{1} \cdot {\beta.}}} & \left. c \right) \\ {T_{2} = {T_{1} \cdot {\beta^{\frac{n_{T} - 1}{n_{T}}}.}}} & \left. d \right) \end{matrix}$
 6. Method for the protection of the centrifugal blowers against the pumping phenomenon comprising the steps of: A) measuring the flow rate processed by the blower (Q), the pressure and temperature of the gas in the inlet section (pi, TI), the revolution number (n) and acquisition of the chemical composition of the gas in inlet; B) individuating the blower pumping flow rate in the effective functioning conditions, by applying the method according to claim 1; C) comparing the individuated pumping flow rate at point B with the processed flow rate individuated at point A, and, in case the difference is lower than a predetermined safety margin, total or partial opening of a gas recirculation valve (2) from the suction delivery.
 7. Method for providing diagnostic signals in order to detect problems of flow rate measurement in the centrifugal blowers, or problems of mechanic or instrumental type, to be used with the method for individuating the pumping conditions according to claim 1, comprising the following steps: Calculating the expected delivery pressure (p2_(EXP)) and of the expected delivery temperature (T2_(EXP)); Detecting if the expected delivery pressure (p2_(EXP)) is different from the measured delivery pressure (p2_(MEAB)), and/or the expected delivery temperature (T2_(EXP)) is different from the measured delivery temperature (T2_(MEAB)), then (p2_(EXP)≠p2_(MEAB) or T2_(EXP)≠T2_(MEAB)) Calculating the expected flow rate according to the measured delivery pressure (Q_(EXP)@P2_(MEAB)) by means of dimensional performance maps of the blower, upgraded to the current inlet conditions according to the method of claim 1; Calculating the expected flow rate according to the measured delivery temperature (Q_(EXP)@T2_(MEAB)) by means of dimensional performance maps of the blower, upgraded to the current inlet conditions according to the method of claim
 1. If Q_(EXP)@P2_(MEAB)=Q_(EXP)@P2_(MEAB) then (D2) providing a diagnostic signal concerning the measure equipment of the flow rate and indicating an instrumental problem about the flow rate reading; Substituting the flow rate acquired at point a) of claim 1 with the expected flow rate according to the measured delivery pressure (Q_(EXP)@P2_(MEAB)) Otherwise (Q_(EXP)@P2_(MEAB)≠Q_(EXP)@P2_(MEAB)) If Q_(EXP)@P2_(MEAB)>Q_(EXP)@T2_(MEAB) then (D3) diagnostic signal indicating a mechanic problem on the blower, i.e. a reduction in the polytropic yield. Otherwise (Q_(EXP)@P2_(MEAB)<Q_(EXP)@T2_(MEAB)) (D4) diagnostic signal indicating a problem on the equipment for the acquisition of the parameters reported at point a) of claim
 1. Otherwise (p2_(EXP)=p2_(MEAB) and T2_(EXP)=T2_(MEAB)) (D1) diagnostic signal of the correct functioning of the blower, i.e. the detection of the performance complying to those expected according to the described method.
 8. Method for the protection of the centrifugal blowers against the pumping phenomenon according to claim 6 further comprising the following steps, carried out simultaneously and independently: acquisition of a signal from a sensor which measures the mechanic vibrations of the blower; frequency analysis of said signal and determination of the intensity of the signal components at the frequencies indicative of the forthcoming pumping condition; comparison of the intensity of said frequency components with the minimum intensity indicative of the pumping conditions or forthcoming pumping; possible partial or total opening of the anti-pumping safety valve.
 9. Method according to claim 8, wherein said frequencies indicative of the forthcoming pumping conditions are comprised between 5 and 20 Hz.
 10. Device for applying the method for the protection of the centrifugal blowers against the pumping phenomenon, comprising: means for measuring the temperature (12) and the pressure (11) of the gas at the blower inlet; means for measuring the flow rate (10) at the blower inlet, means (13) for measuring the number of revolutions of the blower (1); means for measuring the temperature (15) and pressure (14) of the gas in outlet from the blower (1); means (6) for controlling the anti-pumping valve (2) calculation means (16) for carrying out thermodynamic algorithms, interconnected to said means (6) for controlling the anti-pumping means (2).
 11. Device according to claim 10, further comprising means for determining the gas composition.
 12. Device according to claim 10, further comprising means for measuring the vibrations present in the blower running and means for the frequency analysis of said vibrations.
 13. Device according to claim 10, wherein said means for measuring the vibrations comprise a vibration sensor installed near one of the bearings which bear the blower shaft. 